| Elements of mathematics for the geosciences
(objectives)
ELEMENTS OF MATHEMATICS FOR GEOSCIENCES
Provide the algebraic and analytical tools that allow to deal with the three-dimensional space. In particular, introduce differential and integral calculus in multiple variables, and linear algebra in its relationship with geometric thinking. The course will provide the description of some mathematical models through simple differential equations.
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Code
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20411012 |
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Language
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ITA |
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Type of certificate
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Profit certificate
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Credits
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6
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Scientific Disciplinary Sector Code
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MAT/05
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Contact Hours
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24
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Exercise Hours
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36
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Type of Activity
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Basic compulsory activities
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Teacher
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GIULIANI ALESSANDRO
(syllabus)
Integrals of functions of a single variable: definition of definite integrals (limit of Riemann sums, sum of areas with sign); fundamental theorem of integral calculus; primitives and indefinite integrals; integration of elementary functions; integration by parts and by substitution; integration of rational functions; improper integrals.
Functions of several variables: notions of limit, continuity, and partial derivative. Directional derivatives, gradient. Contour lines and lines of maximum slope. Stationary points, maxima, and minima. Hessian matrix. Calculating eigenvalues and eigenvectors of a symmetric matrix.
Curvilinear integrals of vector fields; conservative and non-conservative fields.
Multiple integrals; changes of variables in multiple integrals
Ordinary differential equations: first-order linear equations; equations with separable variables; equilibrium points and their stability; second-order linear differential equations with constant coefficients, homogeneous, and non-homogeneous.
(reference books)
Testi principale di riferimento:
[BEM] D. Benedetto, M. Degli Esposti, C. Maffei: Matematica per le scienze della vita, Ed. Ambrosiana.
[MS] P. Marcellini, C. Sbordone: Elementi di Calcolo, Liguori Editore. In alternativa, degli stessi autori: Calcolo, Liguori Editori.
Testi di esercizi:
[MSes] P.Marcellini, C.Sbordone: Esercitazioni di matematica, vol. primo, parti prima e seconda, Ed. Liguori.
[SS] S. Salsa, A. Squellati: Esercizi di Matematica - Calcolo infinitesimale e algebra lineare, Zanichelli.
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Dates of beginning and end of teaching activities
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From to |
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Delivery mode
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Traditional
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Attendance
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not mandatory
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Evaluation methods
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Written test
Oral exam
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Teacher
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BARBIERI MARCO
(syllabus)
Integrals of functions of a single variable: definition of definite integrals (limit of Riemann sums, sum of areas with sign); fundamental theorem of integral calculus; primitives and indefinite integrals; integration of elementary functions; integration by parts and by substitution; integration of rational functions; improper integrals.
Functions of several variables: notions of limit, continuity, and partial derivative. Directional derivatives, gradient. Contour lines and lines of maximum slope. Stationary points, maxima, and minima. Hessian matrix. Calculating eigenvalues and eigenvectors of a symmetric matrix.
Curvilinear integrals of vector fields; conservative and non-conservative fields.
Multiple integrals; changes of variables in multiple integrals
Ordinary differential equations: first-order linear equations; equations with separable variables; equilibrium points and their stability; second-order linear differential equations with constant coefficients, homogeneous, and non-homogeneous.
(reference books)
Testi principale di riferimento:
[BEM] D. Benedetto, M. Degli Esposti, C. Maffei: Matematica per le scienze della vita, Ed. Ambrosiana.
[MS] P. Marcellini, C. Sbordone: Elementi di Calcolo, Liguori Editore. In alternativa, degli stessi autori: Calcolo, Liguori Editori.
Testi di esercizi:
[MSes] P.Marcellini, C.Sbordone: Esercitazioni di matematica, vol. primo, parti prima e seconda, Ed. Liguori.
[SS] S. Salsa, A. Squellati: Esercizi di Matematica - Calcolo infinitesimale e algebra lineare, Zanichelli.
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Dates of beginning and end of teaching activities
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From to |
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Delivery mode
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Traditional
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Attendance
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not mandatory
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Università Roma Tre